Soliton excitations in a three-spine alpha-helical protein chain with quintic non-linearity

• The dynamics of three-spine alpha-helical proteins with quintic non-linearity is studied.
• The dynamics is studied in the continuum levels.
• The resulting equations are solved analytically.
• The solution supports the propagation of the energy in the form of solitons in alpha-helical proteins.
• The conditions for modulation instability occurrence and the stability of solitons have been found.

We study the dynamics of a three-spine alpha-helical protein chain with quintic non-linearity. The dynamics is found to be governed by a perturbed three-coupled non-linear Schrödinger (NLS) equation. To investigate the solitonic aspects, we identify a completely integrable three-coupled cubic–quintic NLS equation by deriving the Lax pair of operators associated with it. In addition, we study the modulation instability aspects and obtain the conditions for soliton formation.